Consequences of Special Relativity

### Introduction

Special Relativity follows the basic assumption that the speed of light is constant. However since this hypothesis has so far been proven true, there are many bizarre consequences of Special Relativity that apply due to this.

• The relativity of Simultaneity.
• The equivalence between mass and energy.
• Length contraction.
• Time dilation.
• Mass dilation.

#### Relativity of Simultaneity

Simultaneity can be best described as two events happening at the same time which bear correlation to each other. Not to be confused with coincidence which bears no connection with each event.

Simultaneity itself is a hard concept to describe:

Definition by princeton: "happening or existing or done at the same time"

However through the constancy of light we indeed believe that simultaneity is not true for all reference frames. If simultaneity is not true for all reference frames then it too is relative.

In a three dimensional view it should look something like this:

This can be best explained in a small thought experiment involving a stationary observer and a carriage with two people travelling at a constant speed.

Imagine a train carriage with two people at the opposite ends, equidistant from a light source placed in the middle of the train.

The light source will turn on and each observer will, A on the left side and B on the right will hit a button when they see it turn on. Let's say the train is three light seconds long 9x10^8m and the train is moving at a constant velocity of 0.75c. To the observers inside it will appear that the light they see will reach them at the same time and sure enough a detector on-board will register a simultaneous response, seen below.

On the other hand the observer outside will see the light reach A faster than it hits B.

Seen below.

Conclusively we can now state that the principle of simultaneity is not absolute but relative and does not truly exist. After all, two events happening at the same time with correlation to each other, pfft. Coincidence.

page revision: 1, last edited: 02 Oct 2011 14:46